Let \(X\) be some \(K\) dimensional array of random variables
In Bayesian Learning we ultimately seek the joint distribution of \(X\)
\[ \pi(X) \]
- From this we can derive other quantities of interest, e.g., \[ \begin{aligned} {\rm E}[X] & \equiv \int X \;\pi(X)\; dX \\ {\rm Pr}(X < c) & = F(c) \equiv \int_{-\infty}^c \pi(X) dX, \\ q & = F^{-1}(p) \end{aligned} \]
- These calculations can only be done analytically for the simplest models